Callister - An introduction - 8th edition

20.5 Antiferromagnetism and Ferrimagnetism • 809
Figure 20.8 Schematic representation of antiparallel
alignment of spin magnetic moments for antiferromagnetic
manganese oxide.
Mn 2+
0 2–
20.5 ANTIFERROMAGNETISM AND
FERRIMAGNETISM
Antiferromagnetism
antiferromagnetism
This phenomenon of magnetic moment coupling between adjacent atoms or ions
occurs in materials other than those that are ferromagnetic. In one such group, this
coupling results in an antiparallel alignment; the alignment of the spin moments of
neighboring atoms or ions in exactly opposite directions is termed antiferromagnetism.
Manganese oxide (MnO) is one material that displays this behavior. Manganese
oxide is a ceramic material that is ionic in character, having both Mn 2 and
O 2 ions. No net magnetic moment is associated with the O 2 ions, because there is
a total cancellation of both spin and orbital moments. However, the Mn 2 ions possess
a net magnetic moment that is predominantly of spin origin. These Mn 2 ions
are arrayed in the crystal structure such that the moments of adjacent ions are antiparallel.
This arrangement is represented schematically in Figure 20.8. Obviously,
the opposing magnetic moments cancel one another, and, as a consequence, the
solid as a whole possesses no net magnetic moment.
ferrimagnetism
Ferrimagnetism
Some ceramics also exhibit a permanent magnetization, termed ferrimagnetism. The
macroscopic magnetic characteristics of ferromagnets and ferrimagnets are similar;
the distinction lies in the source of the net magnetic moments. The principles of ferrimagnetism
are illustrated with the cubic ferrites. 2 These ionic materials may be
represented by the chemical formula MFe 2 O 4 , in which M represents any one of
several metallic elements. The prototype ferrite is Fe 3 O 4 , the mineral magnetite,
sometimes called lodestone.
The formula for Fe 3 O 4 may be written as Fe 2 O 2 –(Fe 3 ) 2 (O 2 ) 3 , in which the
Fe ions exist in both 2 and 3 valence states in the ratio of 1:2. A net spin magnetic
moment exists for each Fe 2 and Fe 3 ion, which corresponds to 4 and 5 Bohr
magnetons, respectively, for the two ion types. Furthermore, the O 2 ions are magnetically
neutral. There are antiparallel spin-coupling interactions between the Fe
ions, similar in character to antiferromagnetism. However, the net ferrimagnetic
moment arises from the incomplete cancellation of spin moments.
Cubic ferrites have the inverse spinel crystal structure, which is cubic in symmetry,
and similar to the spinel structure (Section 12.2). (A unit cell for this inverse
spinel structure is shown on the front cover of the book. Red spheres represent
ferrite
2
Ferrite in the magnetic sense should not be confused with the ferrite -iron discussed in
Section 9.18; in the remainder of this chapter, the term ferrite implies the magnetic ceramic.